Explanation

(c) Minimum force required to move a body up a rough inclined plane
$F_{1} = mg(\sin{\theta + \mu\cos{\theta)}}$
Minimum force required to prevent the body from sliding down the rough inclined plane.
$F_{2} = \mu\ mg\cos\theta$
According to question
$F_{1} = 3\ F_{2}$
$\therefore\ \ mg(\sin{\theta + \mu\cos{\theta) = 3(\mu\ mg\cos{\theta)}}}$
$\sin{\theta + \mu\cos{\theta = 3\mu\cos\theta}}$
$\sin{\theta = 2\mu\cos\theta}$
$\tan{\theta = 2\mu = 2 \times \frac{1}{2\sqrt{3}} = \frac{1}{\sqrt{3}} = \tan{30{^\circ}}}$
$\theta = 30{^\circ}$